Video: Using the Properties of Parallelograms to Solve a Problem

Find the lengths of line 𝐢𝐷 and line 𝐷𝐴.

01:44

Video Transcript

Find the lengths of line 𝐢𝐷 and line 𝐷𝐴.

First, we’re interested in line 𝐢𝐷 and, second, line 𝐷𝐴. Before we can determine the lengths of these lines, we need to think about what we know about this figure. Line 𝐷𝐴 is parallel to line 𝐢𝐡. And line 𝐷𝐢 is parallel to line 𝐴𝐡. This tells us that in this shape, opposite sides are parallel. And so we can say that 𝐴𝐡𝐢𝐷 is a parallelogram. And in a parallelogram, opposite sides are equal in length. Line 𝐷𝐢 is opposite line 𝐴𝐡. And therefore, 𝐷𝐢 and 𝐴𝐡 are equal in length. If 𝐷𝐢 equals 𝐴𝐡, then they both measure 15 centimeters. We can also say that line 𝐴𝐷 is opposite line 𝐡𝐢 which makes line 𝐴𝐷 equal to line 𝐡𝐢 and a measure of 13 centimeters. 𝐢𝐷 equals 15 centimeters and 𝐴𝐷 equals 13 centimeters. Notice that we can write the name of the line with the end points in either order. 𝐷𝐴 and 𝐴𝐷 are the same lines, and 𝐢𝐷 and 𝐷𝐢 are also the same lines.

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